In Marvel's Avengers there is, to my knowledge, currently no way to replay the campaign except for deleting your save data or (maybe) signing in with a different profile. They may patch in support for replaying campaign missions or New Game Plus in the future but it's not there now, or if it is it's not easily accessible. But it's also a game that has multiple difficulty settings for the campaign which is generally a way to encourage replay value.
Is this the first time this has ever happened?
Obviously there have been games where you had to start over to replay them, but they almost always allowed you to do so via in game options, even if that was just to start a new save and would erase your old one. While having to go to the system level to delete your save isn't a huge difference in theory, one big difference here is that the single player progress persists with the multiplayer stuff, such as character level and equipment. So deleting your save is very suboptimal here as opposed to something like a single player action game or RPG where having a save near the end of the game isn't that useful.
Obviously there have been other Internet based games that cycled content where you couldn't play older stuff after some period of time, but I can't remember any game with multiple difficulties that didn't let you replay on a higher difficulty once you were finished. Can anyone else?
Also this is clearly a terrible decision by SQEnix, and one they will probably fix, but it's a really bad look. They made this long campaign with lots of cut scenes and stuff and only let you play it once? And they made a game about grinding and replaying levels and then only let you play the best ones once?